Simplify the following expression: $z = \dfrac{9a^2 - 144a + 567}{a - 7} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ z =\dfrac{9(a^2 - 16a + 63)}{a - 7} $ Then we factor the remaining polynomial: $a^2 {-16}a + {63} $ ${-7} {-9} = {-16}$ ${-7} \times {-9} = {63}$ $ (a {-7}) (a {-9}) $ This gives us a factored expression: $\dfrac{9(a {-7}) (a {-9})}{a - 7}$ We can divide the numerator and denominator by $(a + 7)$ on condition that $a \neq 7$ Therefore $z = 9(a - 9); a \neq 7$